So far as I can tell, occasional serious heat problems first started popping up in 2007, when a variety of people reported their iPhones were overheating, in some cases enough that a unit would become too hot to hold. That's from regular use, not cracking the case for a round of hardware hacking. Some users who upgraded firmware this year have found that the devices had problems connecting to Wi-Fi networks, with one solution apparently to put the iPhone into a freezer to cool down.
Complaints about iPhones overheating are still showing up on Apple's own discussion boards, along with complaints about MacBook Pros overheating. One of the explanations for the problem is that supposedly installing certain apps can cause the issue.
In the past, Apple has been known to Apple had a battery exchange for certain laptops because certain Sony lithium-ion batteries were overheating in specific but "rare" circumstances. Of course, when you are selling millions of a device, statistically rare situations may commonly appear. And in 2007, Apple, with the U.S. Consumer Product Safety Commission issued a voluntary recall on an older PowerBook AC adapter. (A search on the CPSC site shows no actions for the iPhone.)
Part of the issue may be that the "exterior of iPhone functions as a cooling surface that transfers heat from inside the unit to the cooler air outside," and so Apple notes that the handset can get warm when being used or charging. (This suggestion, which appears in multiple places on Apple's support site, seems to be the only one that addresses an iPhone getting warm, though perhaps there's something obvious that I'm missing.) But you'd think that most people buying an iPhone had used a handset in the past and would be familiar with how devices can get toasty under similar circumstances. The descriptions of the problems sound as though they get considerably hotter than this.
Apple is hardly the only company that has faced device overheating issues. RIM recently had an issue with the Blackberry Bold that caused NTT DoCoMo to stop selling that smartphone in Japan. But even if a relatively isolated occurrence on the iPhone, it could potentially spur yet another class action suit targeting the product, which must get to be some degree of distraction for management.
Burning house image via Flickr user 111 Emergency, CC 2.0.